Parameter retrieval of small particles in dark-field Fourier ptychography and a rectangle in real-space ptychography.

We present a parameter retrieval method which incorporates prior knowledge about the object into ptychography. The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of a rectangular structure with real-space ptychography. The influence of Poisson noise is discussed in the second part of the paper. The Cramér Rao Lower Bound in both applications is computed and Monte Carlo analysis is used to verify the calculated lower bound. With the computation results we report the lower bound for various noise levels and analyze the correlation of particles in application 1. For application 2 the correlation of parameters of the rectangular structure is discussed.

Improved ptychographic inspection of EUV reticles via inclusion of prior information.

The development of actinic mask metrology tools represents one of the major challenges to be addressed on the roadmap of extreme ultraviolet (EUV) lithography. Technological advancements in EUV lithography result in the possibility to print increasingly fine and highly resolved structures on a silicon wafer; however, the presence of fine-scale defects, interspersed in the printable mask layout, may lead to defective wafer prints. Hence, the development of actinic methods for review of potential defect sites becomes paramount. Here, we report on a ptychographic algorithm that makes use of prior information about the object to be retrieved, generated by means of rigorous computations, to improve the detectability of defects whose dimensions are of the order of the wavelength. The comprehensive study demonstrates that the inclusion of prior information as a regularizer in the ptychographic optimization problem results in a higher reconstruction quality and an improved robustness to noise with respect to the standard ptychographic iterative engine (PIE). We show that the proposed method decreases the number of scan positions necessary to retrieve a high-quality image and relaxes requirements in terms of signal-to-noise ratio (SNR). The results are further compared with state-of-the-art total variation-based ptychographic imaging.

Automatic feature selection in EUV scatterometry.

Scatterometry is an important nonimaging and noncontact method for optical metrology. In scatterometry certain parameters of interest are determined by solving an inverse problem. This is done by minimizing a cost functional that quantifies the discrepancy among measured data and model evaluation. Solving the inverse problem is mathematically challenging owing to the instability of the inversion and to the presence of several local minima that are caused by correlation among parameters. This is a relevant issue, particularly when the inverse problem to be solved requires the retrieval of a high number of parameters. In such cases, methods to reduce the complexity of the problem are to be sought. In this work, we propose an algorithm suitable to automatically determine which subset of the parameters is mostly relevant in the model, and we apply it to the reconstruction of 2D and 3D scatterers. We compare the results with local sensitivity analysis and with the screening method proposed by Morris.

Fast semi-analytical solution of Maxwell's equations in Born approximation for periodic structures.

We propose a fast semi-analytical approach for solving Maxwell's equations in Born approximation based on the Fourier modal method (FMM). We show that, as a result of Born approximation, most matrices in the FMM algorithm become diagonal, thus allowing a reduction of computational complexity from cubic to linear. Moreover, due to the analytical representation of the solution in the vertical direction, the number of degrees of freedom in this direction is independent of the wavelength. The method is derived for planar illumination with two basic polarizations (TE/TM) and an arbitrary 2D geometry infinitely periodic in one horizontal direction.

Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry.

Optical scatterometry is the state of art optical inspection technique for quality control in lithographic process. As such, any boost in its performance carries very relevant potential in semiconductor industry. Recently we have shown that coherent Fourier scatterometry (CFS) can lead to a notably improved sensitivity in the reconstruction of the geometry of printed gratings. In this work, we report on implementation of a CFS instrument, which confirms the predicted performances. The system, although currently operating at a relatively low numerical aperture (NA = 0.4) and long wavelength (633 nm) allows already the reconstruction of the grating parameters with nanometer accuracy, which is comparable to that of AFM and SEM measurements on the same sample, used as reference measurements. Additionally, 1 nm accuracy in lateral positioning has been demonstrated, corresponding to 0.08% of the pitch of the grating used in the actual experiment.

Wafer-based aberration metrology for lithographic systems using overlay measurements on targets imaged from phase-shift gratings.

In this paper, a new methodology is presented to derive the aberration state of a lithographic projection system from wafer metrology data. For this purpose, new types of phase-shift gratings (PSGs) are introduced, with special features that give rise to a simple linear relation between the PSG image displacement and the phase aberration function of the imaging system. By using the PSGs as the top grating in a diffraction-based overlay stack, their displacement can be measured as an overlay error using a standard wafer metrology tool. In this way, the overlay error can be used as a measurand based on which the phase aberration function in the exit pupil of the lithographic system can be reconstructed. In practice, the overlay error is measured for a set of different PSG targets, after which this information serves as input to a least-squares optimization problem that, upon solving, provides estimates for the Zernike coefficients describing the aberration state of the lithographic system. In addition to a detailed method description, this paper also deals with the additional complications that arise when the method is implemented experimentally and this leads to a number of model refinements and a required calibration step. Finally, the overall performance of the method is assessed through a number of experiments in which the aberration state of the lithographic system is intentionally detuned and subsequently estimated by the new method. These experiments show a remarkably good agreement, with an error smaller than 5 mλ, among the requested aberrations, the aberrations measured by the on-tool aberration sensor, and the results of the new wafer-based method.

Scalar diffraction modeling in optical disk recording using wave function assembling.

A new scalar diffraction modeling method for simulating the readout signal of optical disks is described. The information layer is discretized into pixels that are grouped in specific ways to form written and unwritten areas. A set of 2D wave functions resulting from these pixels at the detection aperture is established. A readout signal is obtained via the assembly of wave functions from this set according to the content under the scanning spot. The method allows efficient simulation of jitter noise due to edge deformation of recorded marks, which is important at high densities. It is also capable of simulating a physically irregular mark, thereby helping to understand and optimize the recording process.

Nonlinear signal-processing model for signal generation in multilevel two-dimensional optical storage.

A two-dimensional optical storage (TwoDOS) format with binary modulation is being developed in which channel bits are arranged on a two-dimensional hexagonal lattice [W. M. J. Coene, in Optical Data Storage, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 90-92]. The aim is to increase the capacity by a factor of 2 and the data rate by a factor of 10 over third-generation Blu-ray Disc technology. Following a route similar to that used in one-dimensional conventional optical storage [Jpn. J. Appl. Phys. 42, 1074 (2003)] could lead to a further increase in capacity by the addition of another dimension to writing data, such as the use of multiple levels instead of the two levels (pit and land) used in the binary TwoDOS disk format. We present a nonlinear signal-processing model for signal waveform generation as a function of the M-ary channel symbols, as well as simulated signal readouts for multilevel TwoDOS.

Nonlinear signal-processing model for scalar diffraction in optical recording.

A nonlinear signal-processing model is derived for the optical recording channel based on scalar diffraction theory. In this model, the signal waveform is written in closed form as an explicit function of the channel bits that are stored on an optical disk, thereby comprising both linear and nonlinear terms. Its explicit dependence on the channel bits makes this model well suited for signal-processing purposes. With the model it is also convenient to assess the importance of nonlinear contributions to the signal waveform. The model is applied for one-dimensional optical storage as well as for two-dimensional (2D) optical storage in which bits are arranged on a 2D hexagonal lattice. Signal folding is addressed as a typical nonlinear issue in 2D optical storage and can be eliminated by recording of pit marks of sizes considerably smaller than the size of the hexagonal bit cell. Further simplifications of the model with only a limited number of channel parameters are also derived.